Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Next Number

Stage: 2 Short Challenge Level:

Why do this
problem?

This activity is so simple and yet it requires a good
detective-type mind to explore it. The answer can be expressed in
very many different ways.

Possible approach

You might lead up to this by using simple examples, focusing
on encouraging children to explain how they know what the next
number is each time.

Key questions

Tell me about how you got your answer.

How could you get from this number to the next
one?

Possible extension

You could create some similiar examples, or encourage pupils
to make up their own. It would be interesting to give only two
numbers as a start so that there are many possibilities for
extending the sequence. Encourage children to find as many
different ways of continuing it as they can.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.